I defy anyone to come up with a more intense theatrical experience than Samuel Beckett's Not I. In otherwise complete darkness, a disembodied female mouth, known as Mouth, about eight feet above the stage, delivers a hyper-rapid stream of consciousness, a mixture of reminiscence and evasion, an existentially terrifying babble, hinting at deep trauma and extinction of self.

The key word here is "disembodied", for Beckett said the piece is to be delivered as quickly as possible, "at the speed of thought". It is as close as the theatre will ever get to representing a mental interior. But it is a ruined interior, inspired by the woman covering her ears in Caravaggio's Decollation of St John the Baptist, and the numberless muttering old crones whom one sees in the streets ("Ireland is full of them," Beckett said).

We learned a lot about the theatrics of Not I during yesterday's performance by the Irish actor Lisa Dwan, for the South Bank's 2009 London Literature festival. Not just in the performance, which was more than remarkable, but in the short film in which Billie Whitelaw – sadly, too unwell to appear in person – talked about the role, and her memories of Beckett and his direction; and in the final question-and-answer session, chaired by the theatre critic Michael Coveney.

If Not I is intense for the audience, it is much, much more so for the actor. It is, by immediate consent, the most difficult part an actor can ever be called on to play. For a start, it is very hard to learn. Not only does the text repeat itself, loop in and around itself allusively, it contains very precise instructions on the length of pauses between its disjointed phrases. And then there is the speed of delivery: Jessica Tandy, in its New York premiere, delivered the whole in 24 minutes ("You've ruined my play," Beckett told her in an uncharacteristic moment of ungallantry). Whitelaw did it in 14 and a half; she trained herself to speak so fast by counting clearly to 10 during each tick of the clock that counted in the BBC's Nine O'Clock News. Performing it at the Purcell Room last night, though, Lisa Dwan shaved off four and a half minutes (and, she told me, a further half-minute in rehearsal) while still making every syllable audible.

The Mouth must not move away from its spotlight, a discipline which can only be achieved by physical restraint. To speak at such a pace without pausing for breath requires circular breathing; even more difficult, Dwan says, is managing not to swallow. She ends up, she says, feeling like a pelican. There are other difficulties, too: the face must be blacked out using matte makeup and, in Dwan's case, a pair of tights; she is also blindfolded and has her ears blocked. Whitelaw compared performing the piece to "falling backwards into hell"; Dwan says it is like driving the wrong way down a motorway without any brakes.

And finally, there is the very fact of the performance itself. The Beckett estate guards the texts and monitors performances with the vigilance of a basilisk. To perform this piece is to stand very much in the shadow of Whitelaw, who was patiently but exhaustively coached by Beckett himself. Dwan, in her turn, was coached and advised by Whitelaw; there is the sense of a baton being passed on, a legacy.

The Purcell Room at the South Bank was packed for the performance; not an unsold ticket. (It is sold out again tonight, in its only other performance in the festival.) Dwan has performed the piece before, at the Battersea Arts Centre, but this had the feel of a canonical stage moment. And the performance itself – let us just say there were moments when the hairs went up on the back of one's neck. Whitelaw could not do the Irish accent Beckett heard in his head (it would have been too much like acting, which Beckett abhorred); Dwan has the accent, and the pace. Whitelaw's performance will always be the definitive one, but Dwan, perhaps, has delivered something even closer to Beckett's intentions. It was a privilege to hear her.